If you want to increase the speed of a driven gear, the drive gear should be:

To INCREASE the SPEED of the driven gear, the drive gear should be LARGER than the driven gear. ASVAB Mechanical Comprehension tests gear speed relationships. When a LARGER drive gear turns a SMALLER driven gear, the smaller gear spins FASTER (more rotations) but with LESS torque. Conversely, a small gear driving a large gear turns it slower but with more torque (force). Trade-off: speed vs torque. So for more speed on the driven gear, use a larger drive gear (or smaller driven gear). Gear speed/size relationships are commonly tested.